Calculation of semiclassical free energy differences along non-equilibrium classical trajectories

We have derived several relations, which allow the evaluation of the system free energy changes in the leading order in $\hbar^{2}$ along classically generated trajectories. The results are formulated in terms of purely classical Hamiltonians and trajectories, so that semiclassical partition functions can be computed, e.g., via classical molecular dynamics simulations. The Hamiltonians, however, contain additional potential-energy terms, which are proportional to $\hbar^{2}$ and are temperature-dependent. We discussed the influence of quantum interference on the nonequilibrium work and problems with unambiguous definition of the semiclassical work operator.